1. Topic: Parallel Lines Date: 2010 Objectives: SWBAT…. Determine the angle pair relationship when given two parallel lines cut by a transversalDetermine the angle pair relationship when given two parallel lines cut by a transversal Calculate the missing angle measurements when given two parallel lines cut by a transversalCalculate the missing angle measurements when given two parallel lines cut by a transversal Calculate the missing angle measurements when given two intersecting lines and an angleCalculate the missing angle measurements when given two intersecting lines and an angle

2. Parallel Lines What are Parallel Lines? Parallel lines are lines that lie in the same plane and do not intersect. AB CD Symbol Form: IIABCD

3. Angles and Parallel Lines A transversal is a line that intersects two other lines in two different points. AB CD 12 34 5 6 78 Note that 8 angles are formed.

4. ACTIVITY Determine Angle Relationships formed by Parallel Lines Cut by Transversal AB CD 12 34 5 6 78

5. S T O P !!!! Distribute transparency sheets, parallel lines and record sheet for activity

6. Interior and Exterior Angles AB CD 12 34 5 6 78 Exterior Interior Exterior Interior angles are angles between the parallel lines Exterior angles are angles outside the parallel lines

7. Alternate Interior Angles AB CD 34 5 6 Alternate Interior Angles are equal if two parallel lines are cut by a transversal So  3 and  6 are alternate interior angles and  4 and  5 are alternate interior angles And they are CONGRUENT

8. AB CD 12 78 Alternate Exterior Angles Alternate Exterior Angles are equal if two parallel lines are cut by a transversal So  2 and  7 are alternate exterior angles and  1 and  8 are alternate exterior angles And they are CONGRUENT

9. Corresponding Angles When two lines are cut by a transversal, 4 pairs of corresponding angles are formed. AB CD 12 34 5 6 78 Corresponding angles are congruent!

10. Vertical Angles Vertical angles are always equal. And – you will always have vertical angles wherever two lines intersect! AB CD 12 34 5 6 78

11. Interior Angles on the Same Side are Supplementary AB CD 34 5 6 m  4 + m  6 = 180  m  3 + m  5 = 180 

12. Exterior Angles on the Same Side are Supplementary AB CD 12 7 8 m  1 + m  7 = 180  m  2 + m  8 = 180 

13. AB CD 2 4 78 Adjacent Angles creating a straight line are Supplementary m  2 + m  4 = 180  m  7 + m  8 = 180 

14. Now how do we apply these Angle relationships? AB CD 12 34 5 6 78 1)m  3 = 40˚. Find the m  5. Explain how 2)m  1 = 125˚. Find the m  8. Explain how 3)m  7 = 38˚. Find the m  4. Explain how you determined your answer

15. Summary Alternate Interior Angles are equal Alternate Exterior Angles are equal Corresponding Angles are equal Vertical Angles are equal Interior Angles on the same side are supplementary Exterior Angles on the same side are supplementary Adjacent Angles creating a straight line are supplementary